1.5 killowatt electric heater and 1hp 115v electric motor. Can both run on single 115v 20 amp breaker circuit at same time?

The standard is watts divided by volts equals amps.

Does your electric motor have another rating besides HP rating?

Just with the heater your at 10 amp already.

The heater needs to be on a 20 AMP service by itself. That service has to be sized at 1.25 more than 1500/120.

Is there any other info on the motor nameplate such as FLA?
Motor breakers can be higher than the HP rating because of starting currents. They can differ based on motor construction.

NO! If it's a true 1hp motor you'd need a 25A circuit

Dr. Spa:

Your unclear. What did the "NO" mean. I sized the heater only.

"1.5 killowatt electric heater and 1hp 115v electric motor. Can both run on single 115v 20 amp breaker circuit at same time?"

NO